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MAT240H1 Lecture 4: 240AlgebraI-140917,_Hours_5-6-_The_Complex_Numbers,_vector_spaces.pdf

Canada

Algebra I

Mathematics

Dror Bar- Natan

University of Toronto St. George

: Graphing Complex Numbers. Sketch the complex numbers <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADwAAAAMBAMAAADMqMPsAAAACXBIWXMAAABkAAAAZAAPlsXdAAAAJ1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAB+jSoGAAAADHRSTlMAVTNmIogR5bDMRJnq0HClAAAAmUlEQVQY02NggAFmw2YGPMCVQRyftE4CzwIswtsNFaAscQbuYiEkGRCPJUEYxm1mcGM0QJIG85gEoDxWIEcRyjYNDQ1dAOYpwRQLsjgwKSBbC+IxGrAygC3kUmBkEGYIYESoAPIYnFdOYugAcdzPHGexmqnA0QCTBfEYElgSGBihAmwMbgwMMKdAeCDAiGyjAIbXkR3EhCIDADp9EtuYknvPAAAAAElFTkSuQmCC" class="fm-editor-equation" data-mlang="latex" data-equation="z%2C2z%2C-z">, and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAcBAMAAAB13UkXAAAACXBIWXMAAABkAAAAZAAPlsXdAAAAIVBMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAt9G3DAAAACnRSTlMAZolEVTMi6RHEefPd7AAAAGpJREFUGNNjYGAVZ4ABLmqwGLUUGcgA6iIBDGzGxsYBbA2ODAzMSkpKAgysDjDZUBiDRYAJRDUzMCRaTgXZJjKRoYGtAchKYnCHqolq4DKAqXeHWzARxmASgLFc2BIgDOYAFqhQ+qrlYBoAT7AM10lz28EAAAAASUVORK5CYII=" class="fm-editor-equation" data-mlang="latex" data-equation="%5Cfrac%7B1%7D%7B2%7Dz"> on the same complex plane.<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADYAAAAKBAMAAAAN07A4AAAACXBIWXMAAABkAAAAZAAPlsXdAAAAKlBMVEUAAABHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACpjB07AAAADXRSTlOIAES4M2ZVESLizHeZ4qEztQAAAHVJREFUGNNjEEQGrhMRbJGFDChyghfBpCGEg1/uZJgjNjnxPY4MEoWpgoISDEDAiCInKqzIICiSiGomUN0Eho2C4pVAM11ABoD0bUS1L0CQQSxQAMhQAgJHVLkViQytWksQRgZcCITLmSUyFEoUCqIDsJyEIACfhiPQU4/uGgAAAABJRU5ErkJggg==" class="fm-editor-equation" data-mlang="latex" data-equation="z%3D1%2Bi">

: Graphing Complex Numbers. Sketch the complex numbers <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADwAAAAMBAMAAADMqMPsAAAACXBIWXMAAABkAAAAZAAPlsXdAAAAJ1BMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAB+jSoGAAAADHRSTlMAVTNmIogR5bDMRJnq0HClAAAAmUlEQVQY02NggAFmw2YGPMCVQRyftE4CzwIswtsNFaAscQbuYiEkGRCPJUEYxm1mcGM0QJIG85gEoDxWIEcRyjYNDQ1dAOYpwRQLsjgwKSBbC+IxGrAygC3kUmBkEGYIYESoAPIYnFdOYugAcdzPHGexmqnA0QCTBfEYElgSGBihAmwMbgwMMKdAeCDAiGyjAIbXkR3EhCIDADp9EtuYknvPAAAAAElFTkSuQmCC" class="fm-editor-equation" data-mlang="latex" data-equation="z%2C2z%2C-z">, and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAcBAMAAAB13UkXAAAACXBIWXMAAABkAAAAZAAPlsXdAAAAIVBMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAt9G3DAAAACnRSTlMAZolEVTMi6RHEefPd7AAAAGpJREFUGNNjYGAVZ4ABLmqwGLUUGcgA6iIBDGzGxsYBbA2ODAzMSkpKAgysDjDZUBiDRYAJRDUzMCRaTgXZJjKRoYGtAchKYnCHqolq4DKAqXeHWzARxmASgLFc2BIgDOYAFqhQ+qrlYBoAT7AM10lz28EAAAAASUVORK5CYII=" class="fm-editor-equation" data-mlang="latex" data-equation="%5Cfrac%7B1%7D%7B2%7Dz"> on the same complex plane.<img src="data:image/png;base64,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" class="fm-editor-equation" data-mlang="latex" data-equation="z%3D-1%2Bi%5Csqrt%7B3%7D">

Complex Numbers A complex number is given. Graph the complex number in the complex plane.<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAKBAMAAAAuiOHtAAAACXBIWXMAAABkAAAAZAAPlsXdAAAAKlBMVEVHcEwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHrpZrAAAADXRSTlMAiLsiVUTMZhEz5qR36vhC9wAAAGdJREFUCNdjYGBIYECABAZOIJcdLMQNFoGwGUwVQCQTEpvBAUnIQYHj9AQGlgaEEJDNzh3AYMkAFDIUlBKUYQCxOboYGAoFFwbAVIHYhSDGBYRZQHayA1DTRbgqEFvFAeZGJhiDmQEAl5AQ+pHc/UcAAAAASUVORK5CYII=" class="fm-editor-equation" data-mlang="latex" data-equation="4%2B4i">

MAT240H1 Lecture 4: 240AlgebraI-140917,_Hours_5-6-_The_Complex_Numbers,_vector_spaces.pdf

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